Frontiers in Serre's Modularity Conjecture: Torsion and Low Weights

Workshop dates: 15-19 June 2015Venue: University of Luxembourg, Campus Kirchberg

This workshop aims to create a synergistic environment by bringing together experts with various backgrounds, including specialists on explicit computations, in order to push the frontier on two intriguing aspects of generalisations of Serre's modularity conjectures, namely,

refinements to capture number theoretically significant properties not evident from Betti cohomology (for instance, singling out the case of mod p Galois representations unramified at p), and

exploring number theoretic properties of torsion classes in the cohomology of arithmetic groups yielding real Riemannian manifolds with no complex structure, such as Bianchi groups.